Jordan *-derivation pairs on standard operator algebras and related results

Jordan Maps on Standard Operator Algebras

Jordan isomorphisms of rings are defined by two equations. The first one is the equation of additivity while the second one concerns multiplicativity with respect to the so-called Jordan product. In this paper we present results showing that on standard operator algebras over spaces with dimension at least 2, the bijective solutions of that second equation are automatically additive.

Multiplicative bijective maps on standard operator algebras

Jordan derivation on trivial extension

Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

multiplicative bijective maps on standard operator algebras

Constructive Results on Operator Algebras

We present a to following results in the constructive theory of operator algebras. A representation theorem for finite dimensional von Neumann-algebras. A representation theorem for normal functionals. The spectral measure is independent of the choice of the basis of the underlying Hilbert space. Finally, the double commutant theorem for finite von Neumann algebras and for Abelian von Neumann a...